turk@google.com | 4896f9e | 2009-03-02 20:00:00 +0000 | [diff] [blame^] | 1 | /* |
| 2 | * Copyright (C) 2009 The Android Open Source Project |
| 3 | * |
| 4 | * Licensed under the Apache License, Version 2.0 (the "License"); |
| 5 | * you may not use this file except in compliance with the License. |
| 6 | * You may obtain a copy of the License at |
| 7 | * |
| 8 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 9 | * |
| 10 | * Unless required by applicable law or agreed to in writing, software |
| 11 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 13 | * See the License for the specific language governing permissions and |
| 14 | * limitations under the License. |
| 15 | */ |
| 16 | |
| 17 | #include "SkCubicClipper.h" |
| 18 | #include "SkGeometry.h" |
| 19 | |
| 20 | SkCubicClipper::SkCubicClipper() {} |
| 21 | |
| 22 | void SkCubicClipper::setClip(const SkIRect& clip) { |
| 23 | // conver to scalars, since that's where we'll see the points |
| 24 | fClip.set(clip); |
| 25 | } |
| 26 | |
| 27 | |
| 28 | static bool chopMonoCubicAtY(SkPoint pts[4], SkScalar y, SkScalar* t) { |
| 29 | SkScalar ycrv[4]; |
| 30 | ycrv[0] = pts[0].fY - y; |
| 31 | ycrv[1] = pts[1].fY - y; |
| 32 | ycrv[2] = pts[2].fY - y; |
| 33 | ycrv[3] = pts[3].fY - y; |
| 34 | |
| 35 | #ifdef NEWTON_RAPHSON // Quadratic convergence, typically <= 3 iterations. |
| 36 | // Initial guess. |
| 37 | // TODO(turk): Check for zero denominator? Shouldn't happen unless the curve |
| 38 | // is not only monotonic but degenerate. |
| 39 | #ifdef SK_SCALAR_IS_FLOAT |
| 40 | SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]); |
| 41 | #else // !SK_SCALAR_IS_FLOAT |
| 42 | SkScalar t1 = SkDivBits(ycrv[0], ycrv[0] - ycrv[3], 16); |
| 43 | #endif // !SK_SCALAR_IS_FLOAT |
| 44 | |
| 45 | // Newton's iterations. |
| 46 | const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits. |
| 47 | SkScalar t0; |
| 48 | const int maxiters = 5; |
| 49 | int iters = 0; |
| 50 | bool converged; |
| 51 | do { |
| 52 | t0 = t1; |
| 53 | SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0); |
| 54 | SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0); |
| 55 | SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0); |
| 56 | SkScalar y012 = SkScalarInterp(y01, y12, t0); |
| 57 | SkScalar y123 = SkScalarInterp(y12, y23, t0); |
| 58 | SkScalar y0123 = SkScalarInterp(y012, y123, t0); |
| 59 | SkScalar yder = (y123 - y012) * 3; |
| 60 | // TODO(turk): check for yder==0: horizontal. |
| 61 | #ifdef SK_SCALAR_IS_FLOAT |
| 62 | t1 -= y0123 / yder; |
| 63 | #else // !SK_SCALAR_IS_FLOAT |
| 64 | t1 -= SkDivBits(y0123, yder, 16); |
| 65 | #endif // !SK_SCALAR_IS_FLOAT |
| 66 | converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe |
| 67 | ++iters; |
| 68 | } while (!converged && (iters < maxiters)); |
| 69 | *t = t1; // Return the result. |
| 70 | |
| 71 | // The result might be valid, even if outside of the range [0, 1], but |
| 72 | // we never evaluate a Bezier outside this interval, so we return false. |
| 73 | if (t1 < 0 || t1 > SK_Scalar1) |
| 74 | return false; // This shouldn't happen, but check anyway. |
| 75 | return converged; |
| 76 | |
| 77 | #else // BISECTION // Linear convergence, typically 16 iterations. |
| 78 | |
| 79 | // Check that the endpoints straddle zero. |
| 80 | SkScalar tNeg, tPos; // Parameter where the function is negative and positive, respectively. |
| 81 | if (ycrv[0] < 0) { |
| 82 | if (ycrv[3] < 0) |
| 83 | return false; |
| 84 | tNeg = 0; |
| 85 | tPos = SK_Scalar1; |
| 86 | } else if (ycrv[0] > 0) { |
| 87 | if (ycrv[3] > 0) |
| 88 | return false; |
| 89 | tNeg = SK_Scalar1; |
| 90 | tPos = 0; |
| 91 | } else { |
| 92 | *t = 0; |
| 93 | return true; |
| 94 | } |
| 95 | |
| 96 | const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float. |
| 97 | int iters = 0; |
| 98 | do { |
| 99 | SkScalar tMid = (tPos + tNeg) / 2; |
| 100 | SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid); |
| 101 | SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid); |
| 102 | SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid); |
| 103 | SkScalar y012 = SkScalarInterp(y01, y12, tMid); |
| 104 | SkScalar y123 = SkScalarInterp(y12, y23, tMid); |
| 105 | SkScalar y0123 = SkScalarInterp(y012, y123, tMid); |
| 106 | if (y0123 == 0) { |
| 107 | *t = tMid; |
| 108 | return true; |
| 109 | } |
| 110 | if (y0123 < 0) tNeg = tMid; |
| 111 | else tPos = tMid; |
| 112 | ++iters; |
| 113 | } while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe |
| 114 | |
| 115 | *t = (tNeg + tPos) / 2; |
| 116 | return true; |
| 117 | #endif // BISECTION |
| 118 | } |
| 119 | |
| 120 | |
| 121 | bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) { |
| 122 | bool reverse; |
| 123 | |
| 124 | // we need the data to be monotonically descending in Y |
| 125 | if (srcPts[0].fY > srcPts[2].fY) { |
| 126 | dst[0] = srcPts[3]; |
| 127 | dst[1] = srcPts[2]; |
| 128 | dst[2] = srcPts[1]; |
| 129 | dst[3] = srcPts[0]; |
| 130 | reverse = true; |
| 131 | } else { |
| 132 | memcpy(dst, srcPts, 3 * sizeof(SkPoint)); |
| 133 | reverse = false; |
| 134 | } |
| 135 | |
| 136 | // are we completely above or below |
| 137 | const SkScalar ctop = fClip.fTop; |
| 138 | const SkScalar cbot = fClip.fBottom; |
| 139 | if (dst[2].fY <= ctop || dst[0].fY >= cbot) { |
| 140 | return false; |
| 141 | } |
| 142 | |
| 143 | SkScalar t; |
| 144 | SkPoint tmp[5]; // for SkChopCubicAt |
| 145 | |
| 146 | // are we partially above |
| 147 | if (dst[0].fY < ctop && chopMonoCubicAtY(dst, ctop, &t)) { |
| 148 | SkChopCubicAt(dst, tmp, t); |
| 149 | dst[0] = tmp[2]; |
| 150 | dst[1] = tmp[3]; |
| 151 | } |
| 152 | |
| 153 | // are we partially below |
| 154 | if (dst[2].fY > cbot && chopMonoCubicAtY(dst, cbot, &t)) { |
| 155 | SkChopCubicAt(dst, tmp, t); |
| 156 | dst[1] = tmp[1]; |
| 157 | dst[2] = tmp[2]; |
| 158 | } |
| 159 | |
| 160 | if (reverse) { |
| 161 | SkTSwap<SkPoint>(dst[0], dst[3]); |
| 162 | SkTSwap<SkPoint>(dst[1], dst[2]); |
| 163 | } |
| 164 | return true; |
| 165 | } |
| 166 | |